Convergence of the Nested Multivariate Padé Approximants Original Research Article

The nested multivariate Padé approximants were recently introduced. In the case of two variablesxandy, they consist in applying the Padé approximation with respect to y to the coefficients of the Padé approximation with respect tox. The principal advantage of the method is that the computation only involves univariate Padé approximation. This allows us to obtain uniform convergence where the classical multivariate Padé approximants fail to converge.